package org.matheclipse.core.integrate.rubi45;


import static org.matheclipse.core.expression.F.*;
import static org.matheclipse.core.integrate.rubi45.UtilityFunctionCtors.*;
import static org.matheclipse.core.integrate.rubi45.UtilityFunctions.*;
import org.matheclipse.core.interfaces.IAST;

/** 
 * IndefiniteIntegrationRules from the <a href="http://www.apmaths.uwo.ca/~arich/">Rubi -
 * rule-based integrator</a>.
 *  
 */
public class IntRules43 { 
  public static IAST RULES = List( 
ISetDelayed(Int(Times(Plus(A_DEFAULT,Times(B_DEFAULT,$($s("§sin"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Power(Plus(a_DEFAULT,Times(b_DEFAULT,$($s("§sin"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),m_),Power(Plus(c_DEFAULT,Times(d_DEFAULT,$($s("§sin"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),n_)),x_Symbol),
    Condition(Plus(Times(CN1,Plus(Times(ASymbol,Sqr(b)),Times(CN1,a,b,BSymbol)),Cos(Plus(e,Times(f,x))),Power(Plus(a,Times(b,Sin(Plus(e,Times(f,x))))),Plus(m,C1)),Power(Plus(c,Times(d,Sin(Plus(e,Times(f,x))))),Plus(C1,n)),Power(Times(f,Plus(m,C1),Plus(Times(b,c),Times(CN1,a,d)),Plus(Sqr(a),Negate(Sqr(b)))),-1)),Times(Power(Times(Plus(m,C1),Plus(Times(b,c),Times(CN1,a,d)),Plus(Sqr(a),Negate(Sqr(b)))),-1),Int(Times(Power(Plus(a,Times(b,Sin(Plus(e,Times(f,x))))),Plus(m,C1)),Power(Plus(c,Times(d,Sin(Plus(e,Times(f,x))))),n),Simp(Plus(Times(Plus(Times(a,ASymbol),Times(CN1,b,BSymbol)),Plus(Times(b,c),Times(CN1,a,d)),Plus(m,C1)),Times(b,d,Plus(Times(ASymbol,b),Times(CN1,a,BSymbol)),Plus(m,n,C2)),Times(Plus(Times(ASymbol,b),Times(CN1,a,BSymbol)),Plus(Times(a,d,Plus(m,C1)),Times(CN1,b,c,Plus(m,C2))),Sin(Plus(e,Times(f,x)))),Times(CN1,b,d,Plus(Times(ASymbol,b),Times(CN1,a,BSymbol)),Plus(m,n,C3),Sqr(Sin(Plus(e,Times(f,x)))))),x)),x))),And(And(And(And(And(And(FreeQ(List(a,b,c,d,e,f,ASymbol,BSymbol,n),x),NonzeroQ(Plus(Times(b,c),Times(CN1,a,d)))),NonzeroQ(Plus(Sqr(a),Negate(Sqr(b))))),NonzeroQ(Plus(Sqr(c),Negate(Sqr(d))))),RationalQ(m)),Less(m,CN1)),Not(And(And(IntegerQ(n),Less(n,CN1)),Or(Not(IntegerQ(m)),And(ZeroQ(a),NonzeroQ(c)))))))),
ISetDelayed(Int(Times(Plus(A_DEFAULT,Times(B_DEFAULT,$($s("§cos"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Power(Plus(a_DEFAULT,Times(b_DEFAULT,$($s("§cos"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),m_),Power(Plus(c_DEFAULT,Times(d_DEFAULT,$($s("§cos"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),n_)),x_Symbol),
    Condition(Plus(Times(Plus(Times(ASymbol,Sqr(b)),Times(CN1,a,b,BSymbol)),Sin(Plus(e,Times(f,x))),Power(Plus(a,Times(b,Cos(Plus(e,Times(f,x))))),Plus(m,C1)),Power(Plus(c,Times(d,Cos(Plus(e,Times(f,x))))),Plus(C1,n)),Power(Times(f,Plus(m,C1),Plus(Times(b,c),Times(CN1,a,d)),Plus(Sqr(a),Negate(Sqr(b)))),-1)),Times(Power(Times(Plus(m,C1),Plus(Times(b,c),Times(CN1,a,d)),Plus(Sqr(a),Negate(Sqr(b)))),-1),Int(Times(Power(Plus(a,Times(b,Cos(Plus(e,Times(f,x))))),Plus(m,C1)),Power(Plus(c,Times(d,Cos(Plus(e,Times(f,x))))),n),Simp(Plus(Times(Plus(Times(a,ASymbol),Times(CN1,b,BSymbol)),Plus(Times(b,c),Times(CN1,a,d)),Plus(m,C1)),Times(b,d,Plus(Times(ASymbol,b),Times(CN1,a,BSymbol)),Plus(m,n,C2)),Times(Plus(Times(ASymbol,b),Times(CN1,a,BSymbol)),Plus(Times(a,d,Plus(m,C1)),Times(CN1,b,c,Plus(m,C2))),Cos(Plus(e,Times(f,x)))),Times(CN1,b,d,Plus(Times(ASymbol,b),Times(CN1,a,BSymbol)),Plus(m,n,C3),Sqr(Cos(Plus(e,Times(f,x)))))),x)),x))),And(And(And(And(And(And(FreeQ(List(a,b,c,d,e,f,ASymbol,BSymbol,n),x),NonzeroQ(Plus(Times(b,c),Times(CN1,a,d)))),NonzeroQ(Plus(Sqr(a),Negate(Sqr(b))))),NonzeroQ(Plus(Sqr(c),Negate(Sqr(d))))),RationalQ(m)),Less(m,CN1)),Not(And(And(IntegerQ(n),Less(n,CN1)),Or(Not(IntegerQ(m)),And(ZeroQ(a),NonzeroQ(c)))))))),
ISetDelayed(Int(Times(Plus(A_DEFAULT,Times(B_DEFAULT,$($s("§sin"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Power(Plus(a_DEFAULT,Times(b_DEFAULT,$($s("§sin"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),m_),Power(Plus(c_DEFAULT,Times(d_DEFAULT,$($s("§sin"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),n_)),x_Symbol),
    Condition(Plus(Times(CN1,BSymbol,Cos(Plus(e,Times(f,x))),Power(Plus(a,Times(b,Sin(Plus(e,Times(f,x))))),m),Power(Plus(c,Times(d,Sin(Plus(e,Times(f,x))))),n),Power(Times(f,Plus(m,n,C1)),-1)),Times(Power(Plus(m,n,C1),-1),Int(Times(Power(Plus(a,Times(b,Sin(Plus(e,Times(f,x))))),Plus(m,Negate(C1))),Power(Plus(c,Times(d,Sin(Plus(e,Times(f,x))))),Plus(n,Negate(C1))),Simp(Plus(Times(a,ASymbol,c,Plus(m,n,C1)),Times(BSymbol,Plus(Times(b,c,m),Times(a,d,n))),Times(Plus(Times(BSymbol,Plus(Times(a,c),Times(b,d)),Plus(m,n)),Times(ASymbol,Plus(Times(b,c),Times(a,d)),Plus(m,n,C1))),Sin(Plus(e,Times(f,x)))),Times(Plus(Times(ASymbol,b,d,Plus(m,n,C1)),Times(BSymbol,Plus(Times(a,d,m),Times(b,c,n)))),Sqr(Sin(Plus(e,Times(f,x)))))),x)),x))),And(And(And(And(And(And(FreeQ(List(a,b,c,d,e,f,ASymbol,BSymbol),x),NonzeroQ(Plus(Times(b,c),Times(CN1,a,d)))),NonzeroQ(Plus(Sqr(a),Negate(Sqr(b))))),NonzeroQ(Plus(Sqr(c),Negate(Sqr(d))))),RationalQ(m,n)),Less(Less(C0,m),C1)),Greater(n,CN1)))),
ISetDelayed(Int(Times(Plus(A_DEFAULT,Times(B_DEFAULT,$($s("§cos"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Power(Plus(a_DEFAULT,Times(b_DEFAULT,$($s("§cos"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),m_),Power(Plus(c_DEFAULT,Times(d_DEFAULT,$($s("§cos"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),n_)),x_Symbol),
    Condition(Plus(Times(BSymbol,Sin(Plus(e,Times(f,x))),Power(Plus(a,Times(b,Cos(Plus(e,Times(f,x))))),m),Power(Plus(c,Times(d,Cos(Plus(e,Times(f,x))))),n),Power(Times(f,Plus(m,n,C1)),-1)),Times(Power(Plus(m,n,C1),-1),Int(Times(Power(Plus(a,Times(b,Cos(Plus(e,Times(f,x))))),Plus(m,Negate(C1))),Power(Plus(c,Times(d,Cos(Plus(e,Times(f,x))))),Plus(n,Negate(C1))),Simp(Plus(Times(a,ASymbol,c,Plus(m,n,C1)),Times(BSymbol,Plus(Times(b,c,m),Times(a,d,n))),Times(Plus(Times(BSymbol,Plus(Times(a,c),Times(b,d)),Plus(m,n)),Times(ASymbol,Plus(Times(b,c),Times(a,d)),Plus(m,n,C1))),Cos(Plus(e,Times(f,x)))),Times(Plus(Times(ASymbol,b,d,Plus(m,n,C1)),Times(BSymbol,Plus(Times(a,d,m),Times(b,c,n)))),Sqr(Cos(Plus(e,Times(f,x)))))),x)),x))),And(And(And(And(And(And(FreeQ(List(a,b,c,d,e,f,ASymbol,BSymbol),x),NonzeroQ(Plus(Times(b,c),Times(CN1,a,d)))),NonzeroQ(Plus(Sqr(a),Negate(Sqr(b))))),NonzeroQ(Plus(Sqr(c),Negate(Sqr(d))))),RationalQ(m,n)),Less(Less(C0,m),C1)),Greater(n,CN1)))),
ISetDelayed(Int(Times(Plus(A_DEFAULT,Times(B_DEFAULT,$($s("§sin"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Power(Times(Plus(a_DEFAULT,Times(b_DEFAULT,$($s("§sin"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Plus(c_DEFAULT,Times(d_DEFAULT,$($s("§sin"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))))),-1)),x_Symbol),
    Condition(Plus(Times(Plus(Times(ASymbol,b),Times(CN1,a,BSymbol)),Power(Plus(Times(b,c),Times(CN1,a,d)),-1),Int(Power(Plus(a,Times(b,Sin(Plus(e,Times(f,x))))),-1),x)),Times(Plus(Times(BSymbol,c),Times(CN1,ASymbol,d)),Power(Plus(Times(b,c),Times(CN1,a,d)),-1),Int(Power(Plus(c,Times(d,Sin(Plus(e,Times(f,x))))),-1),x))),And(And(And(FreeQ(List(a,b,c,d,e,f,ASymbol,BSymbol),x),NonzeroQ(Plus(Times(b,c),Times(CN1,a,d)))),NonzeroQ(Plus(Sqr(a),Negate(Sqr(b))))),NonzeroQ(Plus(Sqr(c),Negate(Sqr(d))))))),
ISetDelayed(Int(Times(Plus(A_DEFAULT,Times(B_DEFAULT,$($s("§cos"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Power(Times(Plus(a_DEFAULT,Times(b_DEFAULT,$($s("§cos"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Plus(c_DEFAULT,Times(d_DEFAULT,$($s("§cos"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))))),-1)),x_Symbol),
    Condition(Plus(Times(Plus(Times(ASymbol,b),Times(CN1,a,BSymbol)),Power(Plus(Times(b,c),Times(CN1,a,d)),-1),Int(Power(Plus(a,Times(b,Cos(Plus(e,Times(f,x))))),-1),x)),Times(Plus(Times(BSymbol,c),Times(CN1,ASymbol,d)),Power(Plus(Times(b,c),Times(CN1,a,d)),-1),Int(Power(Plus(c,Times(d,Cos(Plus(e,Times(f,x))))),-1),x))),And(And(And(FreeQ(List(a,b,c,d,e,f,ASymbol,BSymbol),x),NonzeroQ(Plus(Times(b,c),Times(CN1,a,d)))),NonzeroQ(Plus(Sqr(a),Negate(Sqr(b))))),NonzeroQ(Plus(Sqr(c),Negate(Sqr(d))))))),
ISetDelayed(Int(Times(Plus(A_,Times(B_DEFAULT,$($s("§sin"),Plus(c_DEFAULT,Times(d_DEFAULT,x_))))),Power(Times(Sqrt(Plus(a_,Times(b_DEFAULT,$($s("§sin"),Plus(c_DEFAULT,Times(d_DEFAULT,x_)))))),Sqrt($($s("§sin"),Plus(c_DEFAULT,Times(d_DEFAULT,x_))))),-1)),x_Symbol),
    Condition(Times(C4,ASymbol,Power(Times(d,Sqrt(Plus(a,b))),-1),EllipticPi(CN1,Negate(ArcSin(Times(Cos(Plus(c,Times(d,x))),Power(Plus(C1,Sin(Plus(c,Times(d,x)))),-1)))),Times(CN1,Plus(a,Negate(b)),Power(Plus(a,b),-1)))),And(And(And(FreeQ(List(a,b,c,d,ASymbol,BSymbol),x),PositiveQ(b)),PositiveQ(Plus(Sqr(b),Negate(Sqr(a))))),ZeroQ(Plus(ASymbol,Negate(BSymbol)))))),
ISetDelayed(Int(Times(Plus(A_,Times(B_DEFAULT,$($s("§cos"),Plus(c_DEFAULT,Times(d_DEFAULT,x_))))),Power(Times(Sqrt(Plus(a_,Times(b_DEFAULT,$($s("§cos"),Plus(c_DEFAULT,Times(d_DEFAULT,x_)))))),Sqrt($($s("§cos"),Plus(c_DEFAULT,Times(d_DEFAULT,x_))))),-1)),x_Symbol),
    Condition(Times(C4,ASymbol,Power(Times(d,Sqrt(Plus(a,b))),-1),EllipticPi(CN1,ArcSin(Times(Sin(Plus(c,Times(d,x))),Power(Plus(C1,Cos(Plus(c,Times(d,x)))),-1))),Times(CN1,Plus(a,Negate(b)),Power(Plus(a,b),-1)))),And(And(And(FreeQ(List(a,b,c,d,ASymbol,BSymbol),x),PositiveQ(b)),PositiveQ(Plus(Sqr(b),Negate(Sqr(a))))),ZeroQ(Plus(ASymbol,Negate(BSymbol)))))),
ISetDelayed(Int(Times(Plus(A_,Times(B_DEFAULT,$($s("§sin"),Plus(c_DEFAULT,Times(d_DEFAULT,x_))))),Power(Times(Sqrt(Plus(a_,Times(b_DEFAULT,$($s("§sin"),Plus(c_DEFAULT,Times(d_DEFAULT,x_)))))),Sqrt(Times(e_,$($s("§sin"),Plus(c_DEFAULT,Times(d_DEFAULT,x_)))))),-1)),x_Symbol),
    Condition(Times(Sqrt(Sin(Plus(c,Times(d,x)))),Power(Times(e,Sin(Plus(c,Times(d,x)))),CN1D2),Int(Times(Plus(ASymbol,Times(BSymbol,Sin(Plus(c,Times(d,x))))),Power(Times(Sqrt(Sin(Plus(c,Times(d,x)))),Sqrt(Plus(a,Times(b,Sin(Plus(c,Times(d,x))))))),-1)),x)),And(And(And(FreeQ(List(a,b,c,d,e,ASymbol,BSymbol),x),PositiveQ(b)),PositiveQ(Plus(Sqr(b),Negate(Sqr(a))))),ZeroQ(Plus(ASymbol,Negate(BSymbol)))))),
ISetDelayed(Int(Times(Plus(A_,Times(B_DEFAULT,$($s("§cos"),Plus(c_DEFAULT,Times(d_DEFAULT,x_))))),Power(Times(Sqrt(Plus(a_,Times(b_DEFAULT,$($s("§cos"),Plus(c_DEFAULT,Times(d_DEFAULT,x_)))))),Sqrt(Times(e_,$($s("§cos"),Plus(c_DEFAULT,Times(d_DEFAULT,x_)))))),-1)),x_Symbol),
    Condition(Times(Sqrt(Cos(Plus(c,Times(d,x)))),Power(Times(e,Cos(Plus(c,Times(d,x)))),CN1D2),Int(Times(Plus(ASymbol,Times(BSymbol,Cos(Plus(c,Times(d,x))))),Power(Times(Sqrt(Cos(Plus(c,Times(d,x)))),Sqrt(Plus(a,Times(b,Cos(Plus(c,Times(d,x))))))),-1)),x)),And(And(And(FreeQ(List(a,b,c,d,e,ASymbol,BSymbol),x),PositiveQ(b)),PositiveQ(Plus(Sqr(b),Negate(Sqr(a))))),ZeroQ(Plus(ASymbol,Negate(BSymbol)))))),
ISetDelayed(Int(Times(Plus(A_DEFAULT,Times(B_DEFAULT,$($s("§sin"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Power(Times(Sqrt(Plus(a_,Times(b_DEFAULT,$($s("§sin"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))))),Sqrt(Plus(c_DEFAULT,Times(d_DEFAULT,$($s("§sin"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))))),-1)),x_Symbol),
    Condition(Plus(Times(BSymbol,Power(d,-1),Int(Times(Sqrt(Plus(c,Times(d,Sin(Plus(e,Times(f,x)))))),Power(Plus(a,Times(b,Sin(Plus(e,Times(f,x))))),CN1D2)),x)),Times(CN1,Plus(Times(BSymbol,c),Times(CN1,ASymbol,d)),Power(d,-1),Int(Power(Times(Sqrt(Plus(a,Times(b,Sin(Plus(e,Times(f,x)))))),Sqrt(Plus(c,Times(d,Sin(Plus(e,Times(f,x))))))),-1),x))),And(And(And(FreeQ(List(a,b,c,d,e,f,ASymbol,BSymbol),x),NonzeroQ(Plus(Times(b,c),Times(CN1,a,d)))),NonzeroQ(Plus(Sqr(a),Negate(Sqr(b))))),NonzeroQ(Plus(Sqr(c),Negate(Sqr(d))))))),
ISetDelayed(Int(Times(Plus(A_DEFAULT,Times(B_DEFAULT,$($s("§cos"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Power(Times(Sqrt(Plus(a_,Times(b_DEFAULT,$($s("§cos"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))))),Sqrt(Plus(c_DEFAULT,Times(d_DEFAULT,$($s("§cos"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))))),-1)),x_Symbol),
    Condition(Plus(Times(BSymbol,Power(d,-1),Int(Times(Sqrt(Plus(c,Times(d,Cos(Plus(e,Times(f,x)))))),Power(Plus(a,Times(b,Cos(Plus(e,Times(f,x))))),CN1D2)),x)),Times(CN1,Plus(Times(BSymbol,c),Times(CN1,ASymbol,d)),Power(d,-1),Int(Power(Times(Sqrt(Plus(a,Times(b,Cos(Plus(e,Times(f,x)))))),Sqrt(Plus(c,Times(d,Cos(Plus(e,Times(f,x))))))),-1),x))),And(And(And(FreeQ(List(a,b,c,d,e,f,ASymbol,BSymbol),x),NonzeroQ(Plus(Times(b,c),Times(CN1,a,d)))),NonzeroQ(Plus(Sqr(a),Negate(Sqr(b))))),NonzeroQ(Plus(Sqr(c),Negate(Sqr(d))))))),
ISetDelayed(Int(Times(Plus(A_DEFAULT,Times(B_DEFAULT,$($s("§sin"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Sqrt(Plus(a_DEFAULT,Times(b_DEFAULT,$($s("§sin"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))))),Power(Plus(c_DEFAULT,Times(d_DEFAULT,$($s("§sin"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),QQ(-3L,2L))),x_Symbol),
    Condition(Plus(Times(BSymbol,Power(d,-1),Int(Times(Sqrt(Plus(a,Times(b,Sin(Plus(e,Times(f,x)))))),Power(Plus(c,Times(d,Sin(Plus(e,Times(f,x))))),CN1D2)),x)),Times(CN1,Plus(Times(BSymbol,c),Times(CN1,ASymbol,d)),Power(d,-1),Int(Times(Sqrt(Plus(a,Times(b,Sin(Plus(e,Times(f,x)))))),Power(Plus(c,Times(d,Sin(Plus(e,Times(f,x))))),QQ(-3L,2L))),x))),And(And(And(FreeQ(List(a,b,c,d,e,f,ASymbol,BSymbol),x),NonzeroQ(Plus(Times(b,c),Times(CN1,a,d)))),NonzeroQ(Plus(Sqr(a),Negate(Sqr(b))))),NonzeroQ(Plus(Sqr(c),Negate(Sqr(d))))))),
ISetDelayed(Int(Times(Plus(A_DEFAULT,Times(B_DEFAULT,$($s("§cos"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Sqrt(Plus(a_DEFAULT,Times(b_DEFAULT,$($s("§cos"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))))),Power(Plus(c_DEFAULT,Times(d_DEFAULT,$($s("§cos"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),QQ(-3L,2L))),x_Symbol),
    Condition(Plus(Times(BSymbol,Power(d,-1),Int(Times(Sqrt(Plus(a,Times(b,Cos(Plus(e,Times(f,x)))))),Power(Plus(c,Times(d,Cos(Plus(e,Times(f,x))))),CN1D2)),x)),Times(CN1,Plus(Times(BSymbol,c),Times(CN1,ASymbol,d)),Power(d,-1),Int(Times(Sqrt(Plus(a,Times(b,Cos(Plus(e,Times(f,x)))))),Power(Plus(c,Times(d,Cos(Plus(e,Times(f,x))))),QQ(-3L,2L))),x))),And(And(And(FreeQ(List(a,b,c,d,e,f,ASymbol,BSymbol),x),NonzeroQ(Plus(Times(b,c),Times(CN1,a,d)))),NonzeroQ(Plus(Sqr(a),Negate(Sqr(b))))),NonzeroQ(Plus(Sqr(c),Negate(Sqr(d))))))),
ISetDelayed(Int(Times(Plus(A_DEFAULT,Times(B_DEFAULT,$($s("§sin"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Power(Plus(a_DEFAULT,Times(b_DEFAULT,$($s("§sin"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),m_),Power(Plus(c_DEFAULT,Times(d_DEFAULT,$($s("§sin"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),-1)),x_Symbol),
    Condition(Plus(Times(BSymbol,Power(d,-1),Int(Power(Plus(a,Times(b,Sin(Plus(e,Times(f,x))))),m),x)),Times(CN1,Plus(Times(BSymbol,c),Times(CN1,ASymbol,d)),Power(d,-1),Int(Times(Power(Plus(a,Times(b,Sin(Plus(e,Times(f,x))))),m),Power(Plus(c,Times(d,Sin(Plus(e,Times(f,x))))),-1)),x))),And(And(And(FreeQ(List(a,b,c,d,e,f,ASymbol,BSymbol,m),x),NonzeroQ(Plus(Times(b,c),Times(CN1,a,d)))),NonzeroQ(Plus(Sqr(a),Negate(Sqr(b))))),NonzeroQ(Plus(Sqr(c),Negate(Sqr(d))))))),
ISetDelayed(Int(Times(Plus(A_DEFAULT,Times(B_DEFAULT,$($s("§cos"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Power(Plus(a_DEFAULT,Times(b_DEFAULT,$($s("§cos"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),m_),Power(Plus(c_DEFAULT,Times(d_DEFAULT,$($s("§cos"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),-1)),x_Symbol),
    Condition(Plus(Times(BSymbol,Power(d,-1),Int(Power(Plus(a,Times(b,Cos(Plus(e,Times(f,x))))),m),x)),Times(CN1,Plus(Times(BSymbol,c),Times(CN1,ASymbol,d)),Power(d,-1),Int(Times(Power(Plus(a,Times(b,Cos(Plus(e,Times(f,x))))),m),Power(Plus(c,Times(d,Cos(Plus(e,Times(f,x))))),-1)),x))),And(And(And(FreeQ(List(a,b,c,d,e,f,ASymbol,BSymbol,m),x),NonzeroQ(Plus(Times(b,c),Times(CN1,a,d)))),NonzeroQ(Plus(Sqr(a),Negate(Sqr(b))))),NonzeroQ(Plus(Sqr(c),Negate(Sqr(d))))))),
ISetDelayed(Int(Times(Plus(A_DEFAULT,Times(B_DEFAULT,$($s("§sin"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Power(Plus(a_DEFAULT,Times(b_DEFAULT,$($s("§sin"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),m_),Power(Plus(c_DEFAULT,Times(d_DEFAULT,$($s("§sin"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),n_DEFAULT)),x_Symbol),
    Condition(Integrate(Times(Power(Plus(a,Times(b,Sin(Plus(e,Times(f,x))))),m),Power(Plus(c,Times(d,Sin(Plus(e,Times(f,x))))),n),Plus(ASymbol,Times(BSymbol,Sin(Plus(e,Times(f,x)))))),x),And(And(And(FreeQ(List(a,b,c,d,e,f,ASymbol,BSymbol,m,n),x),NonzeroQ(Plus(Times(b,c),Times(CN1,a,d)))),NonzeroQ(Plus(Sqr(a),Negate(Sqr(b))))),NonzeroQ(Plus(Sqr(c),Negate(Sqr(d))))))),
ISetDelayed(Int(Times(Plus(A_DEFAULT,Times(B_DEFAULT,$($s("§cos"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Power(Plus(a_DEFAULT,Times(b_DEFAULT,$($s("§cos"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),m_),Power(Plus(c_DEFAULT,Times(d_DEFAULT,$($s("§cos"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),n_DEFAULT)),x_Symbol),
    Condition(Integrate(Times(Power(Plus(a,Times(b,Cos(Plus(e,Times(f,x))))),m),Power(Plus(c,Times(d,Cos(Plus(e,Times(f,x))))),n),Plus(ASymbol,Times(BSymbol,Cos(Plus(e,Times(f,x)))))),x),And(And(And(FreeQ(List(a,b,c,d,e,f,ASymbol,BSymbol,m,n),x),NonzeroQ(Plus(Times(b,c),Times(CN1,a,d)))),NonzeroQ(Plus(Sqr(a),Negate(Sqr(b))))),NonzeroQ(Plus(Sqr(c),Negate(Sqr(d))))))),
ISetDelayed(Int(Times(Sqrt(Plus(a_,Times(b_DEFAULT,$($s("§sin"),Plus(c_DEFAULT,Times(d_DEFAULT,x_)))))),Power(Times(Plus(A_,Times(B_DEFAULT,$($s("§sin"),Plus(c_DEFAULT,Times(d_DEFAULT,x_))))),Sqrt($($s("§sin"),Plus(c_DEFAULT,Times(d_DEFAULT,x_))))),-1)),x_Symbol),
    Condition(Times(CN1,Sqrt(Plus(a,b)),Power(Times(ASymbol,d),-1),EllipticE(ArcSin(Times(Cos(Plus(c,Times(d,x))),Power(Plus(C1,Sin(Plus(c,Times(d,x)))),-1))),Times(CN1,Plus(a,Negate(b)),Power(Plus(a,b),-1)))),And(And(And(FreeQ(List(a,b,c,d,ASymbol,BSymbol),x),ZeroQ(Plus(BSymbol,Negate(ASymbol)))),PositiveQ(b)),PositiveQ(Plus(Sqr(b),Negate(Sqr(a))))))),
ISetDelayed(Int(Times(Sqrt(Plus(a_,Times(b_DEFAULT,$($s("§cos"),Plus(c_DEFAULT,Times(d_DEFAULT,x_)))))),Power(Times(Plus(A_,Times(B_DEFAULT,$($s("§cos"),Plus(c_DEFAULT,Times(d_DEFAULT,x_))))),Sqrt($($s("§cos"),Plus(c_DEFAULT,Times(d_DEFAULT,x_))))),-1)),x_Symbol),
    Condition(Times(Sqrt(Plus(a,b)),Power(Times(ASymbol,d),-1),EllipticE(ArcSin(Times(Sin(Plus(c,Times(d,x))),Power(Plus(C1,Cos(Plus(c,Times(d,x)))),-1))),Times(CN1,Plus(a,Negate(b)),Power(Plus(a,b),-1)))),And(And(And(FreeQ(List(a,b,c,d,ASymbol,BSymbol),x),ZeroQ(Plus(BSymbol,Negate(ASymbol)))),PositiveQ(b)),PositiveQ(Plus(Sqr(b),Negate(Sqr(a))))))),
ISetDelayed(Int(Times(Sqrt(Plus(a_,Times(b_DEFAULT,$($s("§sin"),Plus(c_DEFAULT,Times(d_DEFAULT,x_)))))),Power(Times(Plus(A_,Times(B_DEFAULT,$($s("§sin"),Plus(c_DEFAULT,Times(d_DEFAULT,x_))))),Sqrt($($s("§sin"),Plus(c_DEFAULT,Times(d_DEFAULT,x_))))),-1)),x_Symbol),
    Condition(Times(CN1,Plus(a,b),Sqrt(Plus(C1,Sin(Plus(c,Times(d,x))))),Sqrt(Times(Plus(a,Times(b,Sin(Plus(c,Times(d,x))))),Power(Times(Plus(a,b),Plus(C1,Sin(Plus(c,Times(d,x))))),-1))),Power(Times(ASymbol,d,Sqrt(Plus(a,Times(b,Sin(Plus(c,Times(d,x))))))),-1),EllipticE(ArcSin(Times(Cos(Plus(c,Times(d,x))),Power(Plus(C1,Sin(Plus(c,Times(d,x)))),-1))),Times(CN1,Plus(a,Negate(b)),Power(Plus(a,b),-1)))),And(And(FreeQ(List(a,b,c,d,ASymbol,BSymbol),x),ZeroQ(Plus(BSymbol,Negate(ASymbol)))),NonzeroQ(Plus(Sqr(a),Negate(Sqr(b))))))),
ISetDelayed(Int(Times(Sqrt(Plus(a_,Times(b_DEFAULT,$($s("§cos"),Plus(c_DEFAULT,Times(d_DEFAULT,x_)))))),Power(Times(Plus(A_,Times(B_DEFAULT,$($s("§cos"),Plus(c_DEFAULT,Times(d_DEFAULT,x_))))),Sqrt($($s("§cos"),Plus(c_DEFAULT,Times(d_DEFAULT,x_))))),-1)),x_Symbol),
    Condition(Times(Plus(a,b),Sqrt(Plus(C1,Cos(Plus(c,Times(d,x))))),Sqrt(Times(Plus(a,Times(b,Cos(Plus(c,Times(d,x))))),Power(Times(Plus(a,b),Plus(C1,Cos(Plus(c,Times(d,x))))),-1))),Power(Times(ASymbol,d,Sqrt(Plus(a,Times(b,Cos(Plus(c,Times(d,x))))))),-1),EllipticE(ArcSin(Times(Sin(Plus(c,Times(d,x))),Power(Plus(C1,Cos(Plus(c,Times(d,x)))),-1))),Times(CN1,Plus(a,Negate(b)),Power(Plus(a,b),-1)))),And(And(FreeQ(List(a,b,c,d,ASymbol,BSymbol),x),ZeroQ(Plus(BSymbol,Negate(ASymbol)))),NonzeroQ(Plus(Sqr(a),Negate(Sqr(b))))))),
ISetDelayed(Int(Times(Sqrt(Plus(a_,Times(b_DEFAULT,$($s("§sin"),Plus(c_DEFAULT,Times(d_DEFAULT,x_)))))),Power(Times(Plus(A_,Times(B_DEFAULT,$($s("§sin"),Plus(c_DEFAULT,Times(d_DEFAULT,x_))))),Sqrt(Times(e_,$($s("§sin"),Plus(c_DEFAULT,Times(d_DEFAULT,x_)))))),-1)),x_Symbol),
    Condition(Times(Sqrt(Sin(Plus(c,Times(d,x)))),Power(Times(e,Sin(Plus(c,Times(d,x)))),CN1D2),Int(Times(Sqrt(Plus(a,Times(b,Sin(Plus(c,Times(d,x)))))),Power(Times(Sqrt(Sin(Plus(c,Times(d,x)))),Plus(ASymbol,Times(ASymbol,Sin(Plus(c,Times(d,x)))))),-1)),x)),And(And(FreeQ(List(a,b,c,d,e,ASymbol,BSymbol),x),ZeroQ(Plus(BSymbol,Negate(ASymbol)))),NonzeroQ(Plus(Sqr(a),Negate(Sqr(b))))))),
ISetDelayed(Int(Times(Sqrt(Plus(a_,Times(b_DEFAULT,$($s("§cos"),Plus(c_DEFAULT,Times(d_DEFAULT,x_)))))),Power(Times(Plus(A_,Times(B_DEFAULT,$($s("§cos"),Plus(c_DEFAULT,Times(d_DEFAULT,x_))))),Sqrt(Times(e_,$($s("§cos"),Plus(c_DEFAULT,Times(d_DEFAULT,x_)))))),-1)),x_Symbol),
    Condition(Times(Sqrt(Cos(Plus(c,Times(d,x)))),Power(Times(e,Cos(Plus(c,Times(d,x)))),CN1D2),Int(Times(Sqrt(Plus(a,Times(b,Cos(Plus(c,Times(d,x)))))),Power(Times(Sqrt(Cos(Plus(c,Times(d,x)))),Plus(ASymbol,Times(ASymbol,Cos(Plus(c,Times(d,x)))))),-1)),x)),And(And(FreeQ(List(a,b,c,d,e,ASymbol,BSymbol),x),ZeroQ(Plus(BSymbol,Negate(ASymbol)))),NonzeroQ(Plus(Sqr(a),Negate(Sqr(b))))))),
ISetDelayed(Int(Times(Power(Times(Plus(A_,Times(B_DEFAULT,$($s("§sin"),Plus(c_DEFAULT,Times(d_DEFAULT,x_))))),Sqrt(Plus(a_DEFAULT,Times(b_DEFAULT,$($s("§sin"),Plus(c_DEFAULT,Times(d_DEFAULT,x_))))))),-1),Sqrt(Times(e_DEFAULT,$($s("§sin"),Plus(c_DEFAULT,Times(d_DEFAULT,x_)))))),x_Symbol),
    Condition(Plus(Times(a,e,Power(Times(ASymbol,Plus(a,Negate(b))),-1),Int(Power(Times(Sqrt(Times(e,Sin(Plus(c,Times(d,x))))),Sqrt(Plus(a,Times(b,Sin(Plus(c,Times(d,x))))))),-1),x)),Times(CN1,e,Power(Plus(a,Negate(b)),-1),Int(Times(Sqrt(Plus(a,Times(b,Sin(Plus(c,Times(d,x)))))),Power(Times(Sqrt(Times(e,Sin(Plus(c,Times(d,x))))),Plus(ASymbol,Times(BSymbol,Sin(Plus(c,Times(d,x)))))),-1)),x))),And(And(FreeQ(List(a,b,c,d,e,ASymbol,BSymbol),x),ZeroQ(Plus(ASymbol,Negate(BSymbol)))),NonzeroQ(Plus(Sqr(a),Negate(Sqr(b))))))),
ISetDelayed(Int(Times(Power(Times(Plus(A_,Times(B_DEFAULT,$($s("§cos"),Plus(c_DEFAULT,Times(d_DEFAULT,x_))))),Sqrt(Plus(a_DEFAULT,Times(b_DEFAULT,$($s("§cos"),Plus(c_DEFAULT,Times(d_DEFAULT,x_))))))),-1),Sqrt(Times(e_DEFAULT,$($s("§cos"),Plus(c_DEFAULT,Times(d_DEFAULT,x_)))))),x_Symbol),
    Condition(Plus(Times(a,e,Power(Times(ASymbol,Plus(a,Negate(b))),-1),Int(Power(Times(Sqrt(Times(e,Cos(Plus(c,Times(d,x))))),Sqrt(Plus(a,Times(b,Cos(Plus(c,Times(d,x))))))),-1),x)),Times(CN1,e,Power(Plus(a,Negate(b)),-1),Int(Times(Sqrt(Plus(a,Times(b,Cos(Plus(c,Times(d,x)))))),Power(Times(Sqrt(Times(e,Cos(Plus(c,Times(d,x))))),Plus(ASymbol,Times(BSymbol,Cos(Plus(c,Times(d,x)))))),-1)),x))),And(And(FreeQ(List(a,b,c,d,e,ASymbol,BSymbol),x),ZeroQ(Plus(ASymbol,Negate(BSymbol)))),NonzeroQ(Plus(Sqr(a),Negate(Sqr(b)))))))
  );
}
